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An 8-sided die is formed when two square pyramids are attached by their bases. The perimeter of the base shape is 6 centimeters. The distance between the tallest points of the two pyramids is 2 centimeters.
What is the surface area of the 8-sided figure?
3.75 square centimeters
6 square centimeters
7.5 square centimeters
12 square centimeters
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Perimeter 6 cm → square side s = 6/4 = 1.5 cm.
Distance between apexes 2 cm → each pyramid height h = 1 cm.
Slant height of a triangular face: l = sqrt(h^2 + (s/2)^2) = sqrt(1^2 + 0.75^2) = sqrt(1.5625) = 1.25 cm.
Area of one triangular face = (1/2)·s·l = 0.5·1.5·1.25 = 0.9375 cm^2.
There are 8 such faces, so total surface area = 8·0.9375 = 7.5 cm^2.
Answer: 7.5 square centimeters.
Distance between apexes 2 cm → each pyramid height h = 1 cm.
Slant height of a triangular face: l = sqrt(h^2 + (s/2)^2) = sqrt(1^2 + 0.75^2) = sqrt(1.5625) = 1.25 cm.
Area of one triangular face = (1/2)·s·l = 0.5·1.5·1.25 = 0.9375 cm^2.
There are 8 such faces, so total surface area = 8·0.9375 = 7.5 cm^2.
Answer: 7.5 square centimeters.
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